Problem: What do the following two equations represent? $-x-y = 5$ $3x+3y = -2$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-x-y = 5$ $-y = x+5$ $y = -1x - 5$ Putting the second equation in $y = mx + b$ form gives: $3x+3y = -2$ $3y = -3x-2$ $y = -1x - \dfrac{2}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.